1
Ehud Meron Department of Solar Energy & Environmental Physics and Physics Department Ben-Gurion University of the Negev A wide scope problem – most drylands, which occupy about 2/5 of the Earth’s terrestrial area and are home to about 1/3 of the human population are susceptible to desertification. Involves four research directions: 1.Understanding desertification 2.Devising warning signals 3.Preventive measures 4.Reversing desertification Desertification - an irreversible decrease in biological productivity induced by climatic variations and anthropogenic disturbances What can pattern formation theory tell us about desertification and restoration of degraded landscapes? Spatio-Temporal Dynamics in Ecology 8-12 December 2014, Leiden Claim: The concepts and tools of pattern formation theory are crucial for understanding desertification and restoration Desertification in the northern Negev

7
Rather than a global shift to the alternative stable state, local domains of the alternative state can form. Ben Gurion University, Ehud Meron - Desertification: what pattern formation theory can tell us? The common view of desertification: unproductive state productive state pfpf p pcpc Subsequent dynamics – transition-zone or front dynamics General results for uniform states: Single fronts - propagate in general productive unproductive space Does not capture an important aspect - disturbances are likely to be local: Three aspects of front dynamics: 1.Dynamics of a single front 2.Front interactions 3.Front instabilities

12
Desertification: the Namibian fairy-circle ecosystem Ben Gurion University, Ehud Meron - Any indications of such processes in the NFC ecosystem? Birth of FC Tschinkel, PLoS ONE 2012 Death of FC Instances of hybrid-state transitions This suggests another form of gradual desertification in a fluctuating environment - temporal escapes outside the snaking range where fronts are not pinned Front propagation then leads to the creation of additional gaps and to a cascade of hybrid state transitions to lower-productivity states. Uniform vegetation Periodic pattern (Gandhi, Knobloch & Beaume 2015).

14
Reversing desertification - a spatial resonance problem Ben Gurion University, Ehud Meron - The common approach: water harvesting by ground modulations, e.g. periodic stripe-like embankments that capture runoff and along which the vegetation is planted. Since the unmodulated system tends anyway to form patterns, this is a spatial resonance problem analogous to temporally forced oscillatory systems. Implicit in this approach is the intuitive assumption that vegetation growth is likely to follow the template of favorable growth conditions dictated by the periodic ground modulations, and form a 1:1 resonant pattern - vegetation band at each embankment.

15
Restoration by water harvesting can fail Ben Gurion University, Ehud Meron - Restoration in the northern Negev by the JNF-KKL Question: is this the best restoration practice? Are there other practices more resilient to environmental fluctuations?

20
Amplitude equations Ben Gurion University, Ehud Meron - Relatively easy for simple models (e.g. the forced SH), much harder for the vegetation model, but the amplitude equations are universal and their structural form should apply to the vegetation context too. Use the amplitude equations to study the mechanism of the collapse process. Indeed they give a similar bifurcation diagram p Rhombic pattern Stripe pattern Bare soil

22
Conclusion Ben Gurion University, Ehud Meron - Restoration by water harvesting as a spatial resonance problem: restoring in a resonant 2d rhombic pattern is more resilient to droughts in comparison with the classical 1:1 stripe restoration. The NFC ecosystem as a case study: being uniform,undisturbed and describable by a relatively simple model, the NFC is an excellent case study for studying vegetation pattern formation and desertification. Desertification is not necessarily abrupt – can occur gradually by front propagation. pfpf pmpm productive unproductive p Bistability of uniform states productive less productive p Bistability of uniform and patterned states Repulsive front interactions  incipient shifts Less is more: less intervention, less areal coverage, more resilience.